Use a stick edger that's all I can think of. You will have to put a little dirt in the area to fill it back in

 

You sure it's from the edger alone? If you haven't had rain in a while your soil could just be retracting away from the concrete.

 

It's something that just happens over time when they use a strong trimmer and not a stick edger. They keep the line against the grass, rather than against the concrete. Grass won't eat up line like concrete will, so they save money. So over time that line moves further and further back towards your yard.

It's just so they can move quicker, cheaper, and have more obvious to the eye results.

Edge yourself, or have the conversation with them about what your seeing.

 

Thank you for the input. I will address the issue with the landscaper and also add some soil.